Week 3 Solutions of equations involving Absolute values

we are going to learn how to solve absolute value inequalities using the standard approach usually taught in an algebra class. That is, learn the rules and apply it correctly. There are four cases involved when solving absolute value inequalities.

 
 

CASE 1:

|x| < a or |x| ≤ a

 

If |x| < a, write as -a < x < a; If |x| ≤ a, write as -a ≤ x ≤ a

 

CASE 2:

|x| > a or |x| ≥ a

 

If |x| > a, write as x < -a or x > a; If |x| ≥ a, write as x ≤ -a or x ≥ a

Solutions of equations involving Absolute values, Interval and types of interval